Influence of rock property correlation on reliability analysis of rock slope stability: From property characterization to reliability analysis

Cohesion (c) and friction angle (ϕ) of rock are important parameters required for reliability analysis of rock slope stability. There is correlation between c and ϕ which affects results of reliability analysis of rock slope stability. However, the characterization of joint probability distribution of c and ϕ through which their correlation can be estimated requires a large amount of rock property data, which are often not available for most rock engineering projects. As a result, the correlation between c and ϕ is often ignored or simply assumed during reliability studies, which may lead to bias estimation of failure probability. In probabilistic rock slope stability analysis, the influence of ignoring or simply assuming the correlation of the rock strength parameters (i.e., c and ϕ) on the reliability of rock slopes has not been fully investigated. In this study, a Bayesian approach is developed to characterize the correlation between c and ϕ, and an expanded reliability-based design (RBD) approach is developed to assess the influence of correlation between c and ϕ on reliability of a rock slope. The Bayesian approach characterizes the site-specific joint probability distribution of c and ϕ, and quantifies the correlation between c and ϕ using available limited data pairs of c and ϕ from a rock project. The expanded RBD approach uses the joint probability distribution of c and ϕ obtained through the Bayesian approach as inputs, to determine the reliability of a rock slope. The approach gives insight into the propagation of the correlation between c and ϕ through their joint probability into the reliability analysis, and their influence on the calculated reliability of the rock slope. The approaches may be applied in practice with little additional effort from a conventional analysis. The proposed approaches are illustrated using real c and ϕ data pairs obtained from laboratory tests of fractured rock at Forsmark, Sweden.